Biomedical subjects

Brian K Kendrick

Publications and source records attributed to Brian K Kendrick.

5 recordsLinked to original sources

PubMed2005

Quantum hydrodynamics: capturing a reactive scattering resonance.

The hydrodynamic equations of motion associated with the de Broglie-Bohm formulation of quantum mechanics are solved using a meshless method based upon a moving least-squares approach. An arbitrary Lagrangian-Eulerian frame of reference and a regridding algorithm which adds and deletes computational points are used to maintain a uniform and nearly constant interparticle spacing. The methodology also uses averaged fields to maintain unitary time evolution. The numerical instabilities associated with the formation of nodes in the reflected portion of the wave packet are avoided by adding artificial viscosity to the equations of motion. A new and more robust artificial viscosity algorithm is presented which gives accurate scattering results and is capable of capturing quantum resonances. The methodology is applied to a one-dimensional model chemical reaction that is known to exhibit a quantum resonance. The correlation function approach is used to compute the reactive scattering matrix, reaction probability, and time delay as a function of energy. Excellent agreement is obtained between the scattering results based upon the quantum hydrodynamic approach and those based upon standard quantum mechanics. This is the first clear demonstration of the ability of moving grid approaches to accurately and robustly reproduce resonance structures in a scattering system.

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PubMed2005

How reactants polarization can be used to change and unravel chemical reactivity.

This article presents theoretical methods for the description of the directional effect of reactant rotation on the reactivity of atom-diatom systems and suggests an experiment that could be used to test theoretical predictions. The theory can be used in conjunction with both quantum reactive scattering and quasiclassical trajectory calculations, and is stated in general terms, which allows it to deal with arbitrary reactant polarizations. The illustrative results obtained for the benchmark H + D2 reaction are also presented and show that under experimentally achievable conditions one can largely control reactive cross sections and product state distributions, while at the same time gaining valuable and at times surprising information on the reaction mechanism.

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PubMed2005

Cyclic-N3. II. Significant geometric phase effects in the vibrational spectra.

An accurate theoretical prediction of the vibrational spectra for a pure nitrogen ring (cyclic-N(3)) molecule is obtained up to the energy of the (2)A(2)/(2)B(1) conical intersection. A coupled-channel approach using the hyperspherical coordinates and the recently published ab initio potential energy surface [D. Babikov, P. Zhang, and K. Morokuma, J. Chem. Phys. 121, 6743 (2004)] is employed. Two independent sets of calculations are reported: In the first set, the standard Born-Oppenheimer approximation is used and the geometric phase effects are totally neglected. In the second set, the generalized Born-Oppenhimer approximation is used and the geometric phase effects due to the D(3h) conical intersection are accurately treated. All vibrational states are analyzed and assigned in terms of the normal vibration mode quantum numbers. The magnitude of the geometric phase effect is determined for each state. One important finding is an unusually large magnitude of the geometric phase effects in the cyclic-N(3): it is approximately 100 cm(-1) for the low-lying vibrational states and exceeds 600 cm(-1) for several upper states. On average, this is almost two orders of magnitude larger than in the previously reported studies. This unique example suggests a favorable path to experimental validation.

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PubMed2004

Quantum hydrodynamics: application to N-dimensional reactive scattering.

The quantum hydrodynamic equations associated with the de Broglie-Bohm formulation of quantum mechanics are solved using a new methodology which gives an accurate, unitary, and stable propagation of a time dependent quantum wave packet [B. K. Kendrick, J. Chem. Phys. 119, 5805 (2003)]. The methodology is applied to an N-dimensional model chemical reaction with an activation barrier. A parallel version of the methodology is presented which is designed to run on massively parallel supercomputers. The computational scaling properties of the parallel code are investigated both as a function of the number of processors and the dimension N. A decoupling scheme is introduced which decouples the multidimensional quantum hydrodynamic equations into a set of uncoupled one-dimensional problems. The decoupling scheme dramatically reduces the computation time and is highly parallelizable. Furthermore, the computation time is shown to scale linearly with respect to the dimension N=2,...,100.

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PubMed2004

A new method for solving the quantum hydrodynamic equations of motion: application to two-dimensional reactive scattering.

The de Broglie-Bohm hydrodynamic equations of motion are solved using a meshless method based on a moving least squares approach and an arbitrary Lagrangian-Eulerian frame of reference. A regridding algorithm adds and deletes computational points as needed in order to maintain a uniform interparticle spacing, and unitary time evolution is obtained by propagating the wave packet using averaged fields. The numerical instabilities associated with the formation of nodes in the reflected portion of the wave packet are avoided by adding artificial viscosity to the equations of motion. The methodology is applied to a two-dimensional model collinear reaction with an activation barrier. Reaction probabilities are computed as a function of both time and energy, and are in excellent agreement with those based on the quantum trajectory method.

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